# Maximum Pressure over a Reaction

1. May 20, 2006

### mrjeffy321

I have an exothermic reaction which evolves gas. The change in entropy of the reaction is -837.02 kJ per 3 moles of gas evolved (about -279 kJ/mol). The reaction takes place inside a sealed container with a constant volume [say volume = 4.5 E-3 m3]. We will assume the temperature of the reaction to be a constant 80° C (far hotter than the temperature outside the container) so as to prevent heat energy flowing into the system from the surroundings.

As the reaction proceeds, the gas evolved must be expanded into the atmosphere above at an ever increasing pressure…a process which takes energy. If we assume all the energy comes from the ambient heat inside the system (which in term comes from the change in enthalpy of the reaction), as the pressure above the reaction grows, eventually the rate of reaction will drop to zero (reaction will stop) since it would take more energy than is released in order to expand the gas.
I am trying to solve for the maximum pressure at which the reaction will still take place.

The work done by the system to expand the gas is equal to,
W = ∆P * V
The point at which the reaction would stop would be when the work to expand the gas equals the change in enthalpy of the reaction.

∆H = ∆P * V
279000 Joules = ∆P * (4.5 E-3 Liters),
∆P = 6.2 E7 Pa ~= 612 atm

This would mean that the reaction would proceed until the “atmospheric” pressure was greater than or equal to about 612 atmospheres!
This is an extremely high pressure, far greater than what I would expect, which leads me to believe I made an error on one of the steps.

Does anyone see where I might have gone wrong?

2. May 20, 2006

### Bystander

You're looking for equilibrium pressure over a reaction. Use Gibbs.

3. May 20, 2006

### mrjeffy321

Gibbs Free Energy? OK.

The problem now is that I cannot find the Free energy of formation or the entropy of formation for one of my products of the reaction,
Aluminum Hydroxide, Al(OH)3.
Without this value, all I can do is estimate the actual change in free energy of the reaction. Based on the values I could find of AlCl3 (-628.8 kJ) and Al2O3 (-1582.3 kJ), I figure Al(OH)3 should be somewhere around -1000 kJ/mol.
If this is true, then the change in free energy of the reaction would be somewhere around -577.22 kJ. If I then follow my previous previous process, I would get a pressure of around 4.3 E7 Pa as the max pressure, only slightly less.

Does anyone know the free energy of formation of Aluminum Hydroxide, Al(OH)3 ?

4. May 21, 2006

### GCT

5. May 21, 2006

### mrjeffy321

NIST webbook only seems to have the standard enthalpy of formation of Al(OH)3, not the entropy of free energy value.

I checked my 2000-2001 CRC handbook and there is no entry for Aluminum Hydroxide.

6. May 21, 2006

### GCT

Did you try searching on google? I'm sure it's floating around out there somewhere.

7. May 22, 2006

### mrjeffy321

Yes, of course I tried google as well, but no luck on my first few attemps the other day.

I was able to find a figure which looks reasonable on this site,
http://www.geo.cornell.edu/geology/classes/geo321/Weathering_notes_05.pdf

Gf° = -1151 kJ/mol

which is pretty close to the estimate I made earlier up. Using this figure, I get an over all change in free energy from the reaction of -293.07 kJ/mole of gas produced. This would give me a max pressure of about 6.5 E7 Pa or about 642 atm.
Does this seem like a reasonable answer?

8. May 22, 2006

### Bystander

What's the reaction?

9. May 22, 2006

### mrjeffy321

The specific reaction I am dealing with is,
2 Al(s) + 6 H2O(l) --> 2 Al(OH)3(s) + 3 H2(g)

The reason I am not very confident of my answer of some 600 or so atmospheres of pressure is that in practice, I have noticed an appearent drop on the rate of the reaction when even a slight pressure is allowed to accumulate over the reaction.
I know I am not getting it anywhere near 600 atm (otherwise I would not be hear writting this), but it atleast seems like the reactions slows down a lot when the Hydrogen gas produced is allowed to build up pressure inside the reaction vessel.

10. May 22, 2006

### Bystander

First, you need to make the distinction between chemical kinetics and thermodynamics; second, you need to state a complete thermodynamic description of the system before trying to do an analysis. Six hundred atmospheres? If hydrogen reduction of aluminum oxide were easy, Alcoa and Reynolds wouldn't be buying, or synthesizing cryolite for electrolysis cells.